D. Yan

activity

20172022

collaborators

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5 papers · 1 filter

math.AG2020

Some polynomial maps with Jacobian rank two or three

Dan Yan

In the paper, we first classify all polynomial maps of the form $H = (u (x, y, z), v (x, y, z), h (x, y))$ in the case that $J H$ is nilpotent and $°_{z} v \leq 1$ . After that, we generalize the s…

math.AG2020

On Shamsuddin derivations and the isotropy groups

Dan Yan

In the paper, we give an affirmative answer to the conjecture in \cite{13}. We prove that a Shamsuddin derivation $D$ is simple if and only if $\operatorname{Aut}(K[x,y_1,\allowbre…

math.AG2018

On simple derivations and the group of polynomial automorphisms commuting with certain derivations

Dan Yan

In the paper, we first study the subgroup of $K$ -automorphisms of $K [x_{1}, \dots, x_{n}]$ which commutes with a simple derivation of $K [x_{1}, \dots, x_{n}]$ . We show that the…

math.AG2017

Polynomial maps with nilpotent Jacobians in dimension three II

Dan Yan

In the paper, we first classify all polynomial maps of the form $H = (u (x, y), v (x, y, z), h (x, y))$ in the case that $J H$ is nilpotent and $(°_{y} u, °_{y} h) \leq 3$ , $H (0) = 0$ . Then we classify…

math.AG2017

Polynomial maps with nilpotent Jacobians in dimension three I

Dan Yan

In this paper, we first prove that $u, v, h$ are linearly dependent over $K$ if $J H$ is nilpotent and $H$ has the form: $H = (u (x, y, z), v (u, h), h (x, y))$ with $H (0) = 0$ or $H=(u(x,y)…